Question

If $X$ is a poisson variate such that $P(X=0)=P(X=1)$,then $P(X=2)=$

• A. $\frac{e}{2}$
• B. $\frac{e}{6}$
• C. $\frac{1}{6e}$
• D. $\frac{1}{2e}$

Answer 1

The correct option is D $\frac{1}{2e}$

$P(X=0)=P(X=1)$
P$(0;\mu )=\frac{e^{-\mu }{\mu }^0}{0!}=P(1;\mu )=\frac{e^{-\mu }{\mu }^1}{1!}$
$e^{-\mu }(1-\mu )$ = 0
$\mu =1$
P(X=2) = $\frac{e^{-\mu }{\mu }^2}{2!}=\frac{e^{-1}}{2}=\frac{1}{2e}$